Versatile power flow transformers for compensating power flow in a transmission line

ABSTRACT

A limited-angle power flow transformer implements power flow control in a transmission line of an n-phase power transmission system, where each phase of the power transmission system has a transmission voltage. The transformer has n primary windings, where each primary winding is on a core and receives the transmission voltage of a respective one of the phases of the power transmission system. The transformer also has m secondary windings on the core of each primary winding for a total of m*n secondary windings, where m is less than n. Each secondary winding has a voltage induced thereon by the corresponding primary winding. For each phase, m secondary windings are assigned to the phase. Each assigned secondary winding for the phase is from a different core. For all phases, the secondary windings are assigned from the cores in a balanced manner. For each phase, the secondary windings assigned to the phase are coupled in series for summing the induced voltages formed thereon. The summed voltage is a compensating voltage for the phase, and the compensating voltage is angularly limited with respect to the phase.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to and filed concurrently with: U.S. patentapplication Ser. No. 09/728,982, entitled “VERSATILE POWER FLOWTRANSFORMERS FOR COMPENSATING POWER FLOW IN A TRANSMISSION LINE”; U.S.patent application Ser. No. 09/728,985, entitled “VERSATILE POWER FLOWTRANSFORMERS FOR COMPENSATING POWER FLOW IN A TRANSMISSION LINE”; andU.S. patent application Ser. No. 09/729,006, entitled “VERSATILE POWERFLOW TRANSFORMERS FOR COMPENSATING POWER FLOW IN A TRANSMISSION LINE”,each of which is hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to power flow transformers that compensatepower flow in a transmission line. More particularly, the presentinvention relates to a power flow transformer that is simple, versatile,and relatively inexpensive.

BACKGROUND OF THE INVENTION

Electric power flow through an alternating current transmission line isa function of the line impedance, the magnitudes of the sending-end andthe receiving-end voltages, and the phase angle between such voltages,as shown in FIG. 1. The impedance of the transmission line is typicallyinductive; accordingly, power flow can be decreased by inserting anadditional inductive reactance in series with the transmission line,thereby increasing the effective reactance of the transmission linebetween its two ends. The power flow can also be increased by insertingan additional capacitive reactance in series with the transmission line,thereby decreasing the effective reactance of the transmission linebetween its two ends. The indirect way to emulate an inductive or acapacitive reactance is to inject a voltage in quadrature with theprevailing line current.

The direct method of voltage regulation of a transmission line is to adda compensating voltage vectorially in- or out-of-phase with the voltageof the transmission line at the point of connection. The indirect methodto regulate the line voltage is to connect a capacitor or an inductor inshunt with the transmission line. A shunt-connected capacitor raises theline voltage by way of generated reactive power. A shunt-connectedinductor absorbs reactive power from the line and thus lowers thevoltage. The indirect way to implement a shunt capacitor or inductor isto generate a voltage in phase with the line voltage at the point ofconnection and connect the voltage source to the line through aninductor. Through control action, the generated voltage can be madehigher or lower than the line voltage in order to emulate a capacitor oran inductor. Lastly, inserting a voltage in series with the line and inquadrature with the phase-to-neutral voltage of the transmission linecan change the effective phase angle of the line voltage.

In order to regulate the voltage at any point in a transmission line, anin-phase or an out-of-phase voltage in series with the line is injected.FIG. 2 shows the shunt compensating transformer scheme for voltageregulation in a transmission line. The exciter unit consists of athree-phase Y-connected primary winding, which is impressed with theinitial line voltage, v₁′(i.e., v_(1A)′, v_(1B)′, and V_(C)′). Theshunt-compensating unit consists of a total of six secondary windings(two windings in each phase for a bipolar voltage injection). The lineis regulated at a voltage, v₁ by adding a compensating voltage, v_(11′),either in- or out-of-phase with the line voltage. The bipolarcompensating voltage in any phase is induced in two windings placed onthe same phase of the transformer core. To control the shuntcompensating unit, a reference voltage V₁* is fed to a gate patternlogic which monitors the magnitude V₁′ of the exciter voltage, v₁′, anddetermines the number of turns necessary on the shunt compensating unit.Based on this calculation, an appropriate thyristor valve is switched onin a tap changer (FIG. 3), which puts the required number of turns inseries with the line.

FIG. 3 shows the schematic diagram of a thyristor-controlled tapchanger. A transformer winding is tapped at various places. Each of thetapped points is connected to one side of a back-to-back thyristor(triac) switch. The other sides of all the thyristor switches areconnected together at point A. Depending on which thyristor is on, thevoltage between points A and B can be varied between zero and the fullwinding voltage with desired steps in between. In a mechanical versionof this arrangement, a load tap changer connects with one of a number oftaps to give a variable number of turns between the connected tap andone end of the winding.

A Static VAR Compensator (SVC) consists of a series of inductors andcapacitors as shown in FIG. 4. SVC compensation is achieved by puttingeither inductance or capacitance in the circuit through a thyristorswitch. The level of compensation is determined by adjusting theconduction angle of the thyristor switch.

A static synchronous compensator (STATCOM) is a voltage source converter(VSC) coupled with a transformer as shown in FIG. 5. Such STATCOMinjects an almost sinusoidal current of variable magnitude at the pointof connection with a transmission line. Such injected current is almostin quadrature with the line voltage, thereby emulating an inductive or acapacitive reactance at the point of connection with the transmissionline.

The STATCOM is connected at BUS 1 of the transmission line, which has aninductive reactance, X_(s), and a voltage source, V_(s), at the sendingend and an inductive reactance, X_(r), and a voltage source, V_(r), atthe receiving end, respectively. The STATCOM consists of a harmonicneutralized voltage source converter, VSC1, a magnetic circuit, MC1, acoupling transformer, T1, a mechanical switch, MS1, current and voltagesensors, and a controller. The primary control of VSC1 is such that thereactive current flow through the STATCOM is regulated.

The STATCOM controller operates the VSC such that the phase anglebetween the VSC voltage and the line voltage is dynamically adjusted sothat the STATCOM generates or absorbs desired VAR at the point ofconnection. FIG. 6 shows a simplified diagram of the STATCOM with a VSCvoltage source, E₁, and a tie reactance, X_(TIE), connected to a powersystem with a voltage source, V_(TH), and a Thevenin reactance, X_(TH).When the VSC voltage is higher than the power system voltage, the system“sees” the STATCOM as a capacitive reactance and the STATCOM isconsidered to be operating in a capacitive mode. Similarly, when thepower system voltage is higher than the VSC voltage, the system “sees”the STATCOM as an inductive reactance and the STATCOM is considered tobe operating in an inductive mode.

The effective line reactance is varied directly by using eithermechanically switched or thyristor switched inductors and capacitors,such as those found in a Thyristor Controlled Series Compensator (TCSC)as shown in FIG. 7. The basic implementation of a TCSC consists of oneor a string of capacitor banks, each of which is shunted by a ThyristorControlled Reactor (TCR). In this arrangement, the current through aTCR, which also circulates through the associated capacitor bank, isvaried in order to control the compensating voltage and thus thevariable reactance. A STATCOM and the STATCOM model are disclosed inmore detail in Sen, STATCOM—STATic synchronous COMpensator: Theory,Modeling, and Applications, IEEE Pub. No. 99WM706, hereby incorporatedby reference.

A Static Synchronous Series Compensator (SSSC) is a Voltage SourceConverter coupled with a transformer as shown in FIG. 8. An SSSC injectsan almost sinusoidal voltage, of variable magnitude, in series with atransmission line. This injected voltage is almost in quadrature withthe line current, thereby emulating indirectly an inductive or acapacitive reactance, X_(q), in series with the transmission line asshown in FIG. 9. The compensating reactance, X_(q), has a positive valuewhen emulating a capacitor and a negative value when emulating aninductor. The effective line reactance, X_(eff), has a positive valuewhen being inductive and a negative value when being capacitive.

The SSSC is connected in series with a simple transmission line, whichhas an inductive reactance, X_(s), and a voltage source, V_(s) at thesending-end and an inductive reactance, X_(r), and a voltage source,V_(r), at the receiving-end, respectively. The SSSC consists of aharmonic neutralized Voltage Source Converter, VSC2, a magnetic circuit,MC2, a coupling transformer, T2, a mechanical switch, MS2, oneelectronic switch, ES, current and voltage sensors, and a controller.The primary function of the SSSC is to inject a voltage in series withthe transmission line and in quadrature with the prevailing linecurrent.

FIG. 9 shows a simple power transmission system with an SSSC operatedboth in inductive and in capacitive modes and the related phasordiagrams. The line current decreases from I_(0%) to I_(−100%), when theinductive reactance compensation, −X_(q)/X_(L), increases from 0% to100%. The line current increases from I_(0%) to I_(33%), when thecapacitive reactance compensation, X_(q)/X_(L), increases from 0% to33%. An SSSC and the SSSC model are disclosed in more detail in Sen,SSSC—Static Synchronous Series Compensator: Theory, Modeling, andApplications, IEEE Pub. No. PE-862-PWRD-0-04-1997, hereby incorporatedby reference, and in Gyugyi, Schauder, and Sen, SSSC—Static SynchronousSeries Compensator: A Solid-State Approach to the Series Compensation ofTransmission Lines, IEEE Pub. No. 96WM120-6PWRD, also herebyincorporated by reference.

The effective angle of a transmission line is varied by using a PhaseShifting Transformer, which is also known as a Phase Angle Regulator(PAR). A PAR injects a voltage in series with the transmission line andin quadrature with the phase-to-neutral voltage of the transmission lineas shown in FIG. 10A. The series injected voltage introduces a phaseshift whose magnitude in radian varies with the magnitude of the seriesinjected voltage input where the phase-to-neutral voltage of thetransmission line is the base voltage. In a typical configuration, a PARconsists of two transformers (FIG. 10B). The first transformer in theexciter unit is a regulating transformer that is shunt connected withthe line. The first, regulating transformer primary windings are excitedfrom the line voltage and a voltage is induced in the secondarywindings. A voltage with variable magnitude and in quadrature with theline voltage is generated from the phase-to-phase voltage of the inducedvoltage of the first transformer using taps. For series injection ofthis voltage, an electrical isolation is necessary.

The second transformer in the series unit is a series transformer thatis excited from the phase-to-phase voltage of the regulating transformerand its induced voltage is connected in series with the line. Since theseries injection voltage is only a few percent of the line voltage, theseries transformer can be a step-down transformer. The primary windingof the series transformer as well as the secondary winding of theregulating transformer can be high voltage and low current rated so thatthe taps can operate normally at low current and can ride through highfault current.

In an alternate arrangement as shown in FIG. 10C, the PAR regulates theangle of the transmission line voltage using two transformersmaintaining equal lengths of phasors V₁, and V₂. In another arrangementas shown in FIG. 10D, there may be two series connected windings, whichare dedicated for inducing a compensating voltage for series injectionin each phase. In this way, there are three pairs of electricallyisolated windings for the series unit (one pair for each phase) andthree windings for the exciter unit. This arrangement uses only asingle-core three-phase transformer. However, the taps carry high linecurrent as well as even higher fault current. The capability of the PARshown in FIG. 10D can be achieved in an alternate arrangement shown inFIG. 10E where the exciter unit is delta-connected, which offers fewerwindings and no ground connection.

The characteristics of mechanically switched and Thyristor-controlledPower Flow Controllers are such that each controller can control onlyone of the three transmission parameters (voltage, impedance, andangle). Therefore, changing one parameter affects both the real and thereactive power flow in the transmission line.

The desired operation of an ideal power flow controller is describedbelow. FIG. 11A shows a single line diagram of a simple transmissionline with an inductive reactance, X_(L), and a series insertion voltage,V_(dq), connecting a sending-end voltage source, V_(s), and areceiving-end voltage source, V_(r), respectively. The voltage acrossthe transmission line reactance, X_(L), isV_(x)=V_(s)−V_(r)−V_(dq)=IX_(L) where I is the current in thetransmission line. Changing the insertion voltage, V_(dq), in serieswith the transmission line can change the voltage, V_(x), across thetransmission line and, consequently, the line current and the power flowin the line will change.

Consider the case where V_(dq)=0 (FIG. 11, section (b)). Thetransmission line sending-end voltage, V_(s), leads the receiving-endvoltage, V_(r), by an angle δ. The resulting current in the line is I;the real and the reactive power flow at the receiving end are P and Q,respectively. With an injection of V_(dq) in series with thetransmission line, the transmission line sending-end voltage, V_(o)still leads the receiving-end voltage, V_(r), but by a different angleδ₁ (FIG. 11, section (c)). The resulting line current and power flowchange, as shown. With a larger amount of V_(dq) injected in series withthe transmission line, the transmission line sending-end voltage, V_(o),now lags the receiving-end voltage, V_(r), by an angle δ₂(FIG. 11,section (d)). The resulting line current and the power flow now reverse.Notice that the injected series voltage, V_(dq), is at any angle, Φ,with respect to the line current, I. This necessitates the seriesinjected voltage to exchange both real and reactive power with thetransmission line, which emulates, in series with the line, a capacitoror an inductor and a positive resistor that absorbs real power from theline or a negative resistor that delivers real power to the line. Theresult is that the real and the reactive power flow in the line can beregulated selectively. Recall an SSSC injects a voltage in quadraturewith the line current and, therefore, affects both the real and thereactive power flow in the line simultaneously.

For a desired amount of real and reactive power flow in a line, a singlecompensating voltage with a variable magnitude and at any angle withrespect to the line current should be injected in series with the line.The compensating voltage, being at any angle with the prevailing linecurrent, emulates in series with the transmission line a capacitor, aninductor, a positive resistor that absorbs real power from the line anda negative resistor that delivers real power to the line. Since the linecurrent is at any angle with respect to the line voltage, thecompensating voltage is also at any angle with respect to the linevoltage. Note that the necessary condition to selectively regulate thereal and reactive power flow in the line is that the series injectedvoltage must be at any angle with respect to the prevailing linecurrent. Also note that the series injected voltage in FIG. 9 is at somearbitrary angle with respect to the line voltage, V_(s), but the linecurrent is always in quadrature with the series injected voltage, whichaffects both the real and the reactive power flow in the line at thesame time.

When the STATCOM of FIG. 5 and the SSSC of FIG. 8 operate as stand-alonecompensators, they exchange almost exclusively reactive power at theirterminals. While operating both the VSCs together as a unified powerflow controller (UPFC) with a common DC link capacitor, as shown in FIG.12, the exchanged power at the terminals of each inverter can bereactive as well as real. The exchanged real power at the terminals ofone VSC with the line flows to the terminals of the other VSC throughthe common DC link capacitor. The DC capacitor voltage is defined by thereactive current flowing through the STATCOM. The variable seriesinjected voltage is derived from the DC capacitor voltage and can be atany angle with respect to the line current.

FIG. 12 shows a UPFC connected in series with a simple transmissionline, which has an inductive reactance, X_(s), and a voltage source,V_(s) at the sending-end and an inductive reactance, X_(r), and avoltage source, V_(r), at the receiving-end, respectively. The UPFCconsists of two harmonic neutralized voltage source converters, VSC1 andVSC2, two magnetic circuits, MC1 and MC2, two coupling transformers, T1and T2, four mechanical switches, MS1, MS2, MS3, and MS4, one electronicswitch, ES, current and voltage sensors, and a controller. The VSCs areconnected through a common DC link capacitor. The STATCOM is operated byregulating the reactive current flow through it. The SSSC is operated byinjecting a voltage in series with the transmission line.

FIG. 13 shows a basic UPFC model, which consists of a STATCOM and anSSSC. The SSSC injects a voltage, V_(dq), in series with thetransmission line, which, in turn, changes the voltage, V_(x), acrossthe transmission line and hence the current and the power flow throughthe transmission line change. FIG. 13 also shows a phasor diagram of asimple power transmission system, defining the relationship between thesending-end voltage, V_(s), the receiving-end voltage, V_(r), thevoltage across X_(L), V_(x), and the inserted voltage, V_(dq), withcontrollable magnitude (0≦V_(dq)≦V_(dqmax)) and angle (0≦ρ ≦360°). Theinserted voltage, V_(dq), is added to the fixed sending-end voltage,V_(s), to produce the effective sending-end voltage, V_(o)=V_(s)+V_(dq).The difference, V_(o)−V_(r), provides the compensated voltage, V_(x),across X_(L). As angle ρ is varied over its full 360° range, the end ofphasor V_(dq) moves along a circle with its center located at the end ofphasor V_(s). The rotation of phasor V_(dq) with angle ρ modulates boththe magnitude and the angle of phasor V_(x) and, therefore, both thetransmitted real power, P, and the reactive power, Q, vary with ρ in asinusoidal manner. The phase angle, φ, (FIG. 11, sections (c) and (d))between the injected voltage, V_(dq), and the line current, I, can varybetween 0 and 2π. The component of the injected voltage, which is in orout of phase with the line current, emulates a positive or negativeresistor in series with the transmission line. The remaining component,which is in quadrature with the line current, emulates an inductor or acapacitor in series with the transmission line. This process, of course,requires the compensating voltage, V_(dq), to deliver and absorb bothreal and reactive power, P_(exch) and Q_(exch), which are alsosinusoidal functions of angle ρ (P_(exch) being shown in FIG. 13 sinceonly the real power flows through the DC link capacitor). The exchangedreal power, P_(exch), and reactive power, Q_(exch), by the SSSC with theline are

P _(exch) =V _(dq) ·I=V _(dq)/cosφ=V _(d)/, and

Q _(exch) =V _(dq) ×I=V _(dq)/sinφ=V _(q)/.

Only the exchanged real power, P_(exch), with the line flows through theSTATCOM. This real power flow through the STATCOM results in acorresponding real current, I_(d), flow which is either in-phase orout-of-phase with the line voltage. The loading effect of such realcurrent I_(d) on the power system network may be compensated by theindependent control of the reactive current flow through the STATCOM.This reactive or quadrature component, I_(q), which is in quadraturewith the line voltage, emulates an inductive or a capacitive reactanceat the point of connection with the transmission line. A UPFC and theUPFC model are disclosed in more detail in Sen and Stacey, UPFC—UnifiedPower Flow Controller: Theory, Modeling, and Applications, IEEE Pub. No.PE-282-PWRD-0-12-1997, hereby incorporated by reference.

While the PAR of FIGS. 10A-10E and the UPFC of FIG. 12 are usefulschemes for power flow control in a transmission line of a powertransmission system, it is to be recognized that such schemes aredeficient in such areas as versatility, simplicity, and relative cost.Accordingly, a need exists for a power flow control scheme that is infact more versatile, simpler, and relatively inexpensive.

SUMMARY OF THE INVENTION

In the present invention, the aforementioned need is satisfied by apower flow transformer (PFT) based on the traditional technologies oftransformers and tap changers. By using a PFT, one can selectivelycontrol the real and the reactive power flow in a line and regulate thevoltage of the transmission line. Such PFT generates a compensatingvoltage of line frequency for series injection with a transmission line.Such compensating voltage is extracted from the line voltage and is ofvariable magnitude and at any angle with respect to the line voltage.The compensating voltage is also at any angle with respect to theprevailing line current, which emulates, in series with the line, acapacitor, an inductor, a positive resistor that absorbs real power fromthe line, or a negative resistor that delivers real power to the line.Accordingly, the real and the reactive power flow in a transmission linecan be regulated selectively.

In one embodiment of the present invention, a limited-angle power flowtransformer implements power flow control in a transmission line of ann-phase power transmission system, where each phase of the powertransmission system has a transmission voltage. The transformer has nprimary windings, where each primary winding is on a core and receivesthe transmission voltage of a respective one of the phases of the powertransmission system. The transformer also has m secondary windings onthe core of each primary winding for a total of m*n secondary windings,where m is less than n. Each secondary winding has a voltage inducedthereon by the corresponding primary winding.

For each phase, m secondary windings are assigned to the phase. Eachassigned secondary winding for the phase is from a different core. Forall phases, the secondary windings are assigned from the cores in abalanced manner. For each phase, the secondary windings assigned to thephase are coupled in series for summing the induced voltages formedthereon. The summed voltage is a compensating voltage for the phase, andthe compensating voltage is angularly limited with respect to the phase.

Generally, in the PFT, regulation of a transmission line voltage isachieved by adjusting the number of turns in a nine-winding set by wayof mechanical or solid-state tap changers. Although mechanical tapchangers are quite adequate for most utility applications, dynamicperformance can be improved if need be by employing solid-state tapchangers such as thyristor-controlled switches.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofpreferred embodiments of the present invention, will be betterunderstood when read in conjunction with the appended drawings. For thepurpose of illustrating the invention, there are shown in the drawingsembodiments which are presently preferred. As should be understood,however, the invention is not limited to the precise arrangements andinstrumentalities shown. In the drawings:

FIG. 1 is a schematic diagram showing an elementary power transmissionsystem;

FIG. 2 is a schematic diagram showing a shunt compensating transformerand its control that may be employed in connection with the powertransmission system of FIG. 1;

FIG. 3 is a schematic diagram showing a thyristor-controlled tap changerthat may be employed to control the transformer of FIG. 2;

FIG. 4 is a schematic diagram showing a thyristor-controlled static VARcompensator that may be employed in connection with the powertransmission system of FIG. 1;

FIG. 5 is a schematic diagram showing a static synchronous compensator(STATCOM) that may be employed in connection with the power transmissionsystem of FIG. 1;

FIG. 6 is a schematic diagram showing the static synchronous compensatorof FIG. 5 operating in capacitive and inductive modes;

FIG. 7 is a schematic diagram showing a thyristor-controlled seriescompensator (TCSC) employing a string of m series capacitor banks, eachwith a parallel-connected thyristor-controlled reactor, that may beemployed in connection with the power transmission system of FIG. 1;

FIG. 8 is a schematic diagram showing a static synchronous seriescompensator (SSSC) that may be employed in connection with the powertransmission system of FIG. 1;

FIG. 9 is a schematic diagram showing the static synchronous seriescompensator of FIG. 8 operated in inductive and capacitive modes, andthe related phasor diagrams;

FIG. 10a is a schematic diagram showing power transmission control byphase angle regulator in connection with the power transmission systemof FIG. 1;

FIG. 10b is a schematic diagram showing the phase angle regulator schemeof FIG. 10a with two transformers;

FIG. 10c is a schematic diagram showing the phase angle regulator schemeof FIG. 10a with two transformers maintaining equal lengths of phasorsv₁ and v₂;

FIG. 10d is a schematic diagram showing the phase angle regulator schemeof FIG. 10a with one transformer;

FIG. 10e is a schematic diagram showing the phase angle regulator schemeof FIG. 10a with one transformer and no ground connection;

FIG. 11 is a schematic diagram showing the operation of an ideal powerflow controller and related phasor diagrams;

FIG. 12 is a schematic diagram showing a unified power flow controller(UPFC) that may be employed in connection with the power transmissionsystem of FIG. 1;

FIG. 13 is a schematic diagram showing a basic unified power flowcontroller model in connection with the unified power flow controller ofFIG. 12;

FIG. 14 is a schematic diagram showing a versatile power flowtransformer (VPFT) in accordance with one embodiment of the presentinvention;

FIG. 15 is a schematic diagram showing a control block diagram forimpedance emulation for use in connection with the transformer of FIG.14;

FIG. 16 is a schematic diagram showing a basic versatile power flowtransformer model in connection with the versatile power flowtransformer of FIG. 14;

FIG. 17 is a schematic diagram showing a shunt compensating transformerscheme for voltage regulation in accordance with one embodiment of thepresent invention;

FIG. 18 is a schematic diagram showing a series compensating transformerscheme for voltage and angle regulation in accordance with oneembodiment of the present invention;

FIGS. 19-22 are schematic diagrams showing series compensatingtransformer schemes for voltage and angle regulation between 0 and−120°, 0 and 120°, 120° and 240°, and −60° and 60°, respectively, inaccordance with respective embodiments of the present invention; and

FIG. 23 is a schematic diagram showing a variation on the versatilepower flow transformer (VPFT) of FIG. 14 in accordance with oneembodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Versatile Power Flow Transformer (VPFT)

Referring now to FIG. 14, a Versatile Power Flow Transformer (VPFT) isshown for implementing power flow control in a transmission line of apower transmission system in accordance with one embodiment of thepresent invention. As shown, in the VPFT, the line voltage is appliedacross the primary windings 1A, 1B, 1C in the exciter unit (only winding1A being shown). Each primary winding has three secondary windings inseries, for a total of nine secondary windings—a1, c2 and b3 on the coreof A-phase; b1, a2 and c3 on the core of B-phase; and c1, b2 and a3 onthe core of C-phase. As seen, a compensating voltage for any phase isderived from the vectorial sum of the voltages induced in a three-phasewinding set—a1, a2 and a3 for injection in A-phase; b1, b2 and b3 forinjection in B-phase; and c1, c2 and c3 for injection in C-phase.Importantly, a tap is employed on each of the nine secondary windings sothat each entity in each vectorial sum can be individually magnitudallyvaried. Each tap may be a mechanical or solid-state tap changer such asthe tap changer of FIG. 3, e.g., although other types of taps may beemployed without departing from the spirit and scope of the presentinvention.

For example, and more specifically, the voltage V_(21A) (shown) is thesum of at least a tapped portion of the voltage across a1 as derivedfrom A-phase, at least a tapped portion of the voltage across a2 asderived from B-phase, and at least a tapped portion of the voltageacross a3 as derived from C-phase:

V _(21A)=%x a 1+%y a 2+%z a 3;

and voltage V_(21A) is injected as a compensating voltage in line withv_(1A) to produce compensated voltage V_(2A):

V _(2A) =V _(21A) +V _(1A).

Compensating voltages V_(21B) for the B-phase and V_(21C) for theC-phase are similarly produced:

V _(21B)=%x b 1+%y b 2+%z b3;

V _(2B) =V _(21B) +V _(1B).

V _(21C)=%x c 1+%y c 2+%z c3;

V _(2C) =V _(21C) +V _(1C).

Notably, a1, b1, and c1 should be substantially identical; a2, b2, andc2 should be substantially identical; and a3, b3, and c3 should besubstantially identical. In addition, each of %x, %y, and %z should besubstantially identical across the phases of the VPFT. Accordingly, themagnitude of the produced V_(21A), V_(21B), and V_(21C) should besubstantially identical; and V_(21A), V_(21B), and V_(21C) should besubstantially 120 degrees out of phase with each other, assuming thatv_(1A), v_(1B), and V_(1C) are substantially 120 degrees out of phasewith each other. Accordingly, the transmission lines A, B, and C ascompensated are substantially in balance. Nevertheless, non-identicalvariations of any of the aforementioned values may be employed withoutdeparting from the spirit and scope of the present invention if deemednecessary and/or appropriate.

FIG. 15 shows a control block diagram of a controller for controllingthe series impedance emulation achieved by the VPFT of FIG. 14. Thesteps performed by such controller in one embodiment of the presentinvention are as follows. An instantaneous 3-phase set of line voltages,v₁, (i.e., v_(1A), v_(1B), V_(1C)) is used to calculate the referenceangle, Θ, which is phase-locked to the phase a of the line voltage,v_(1A). From an instantaneous 3-phase set of measured line currents, I,the magnitude, I, and its relative angle, Θ_(ir), with respect to thephase-lock-loop angle, Θ, are calculated. From the compensatingresistance demand, R*, and the compensating reactance demand, X*, bothexternally supplied, the demanded impedance's magnitude, Z*, and angle,Θ_(z), are calculated. The magnitude, I, of the line current multipliedby the compensating impedance demand, Z*, is the insertion voltagemagnitude demand, V_(dq)*. The relative phase angle, β, of thisinsertion voltage demand is Θ_(ir)+Θ_(z).

Once the desired series injection voltage, V_(dq)*, and its angle, β,are defined, the Tap Control Unit in FIG. 15 determines the contributionfrom each winding of a 3-phase set (a1, a2, and a3 for injection inA-phase; b1, b2, and b3 for injection in B-phase; and c1, c2, and c3 forinjection in C-phase) to constitute V_(dq)*. In particular, fromknowledge of the magnitude of the exciter voltage, V₁, the Tap ControlUnit determines the number of turns necessary on each winding of theseries-compensating unit. The actual method of such determination isknown or should be apparent to the relevant public and therefore neednot be discussed herein in any detail. Based on this calculation, theappropriate taps are switched on via an appropriate mechanical or solidstate tap changer (see FIG. 3, e.g.), which accordingly put the requirednumber of turns in series with the line. In addition, a VPFT canregulate the line voltage by utilizing the unused portions of thetransformer windings as a shunt compensating unit, as will be discussedin more detail below. Of course, other methods of controlling the seriesimpedance emulation achieved by the VPFT of FIG. 14 may be employedwithout departing from the spirit and scope of the present invention.

FIG. 16 shows a model of the basic VPFT of FIG. 14 as coupled to asimple power transmission system, and also a phasor diagram of thetransmission system. As seen, in the system the sending-end voltage isV_(s), the receiving-end voltage is V_(r), the voltage across the lineimpedance X_(L), is V_(x), and the inserted voltage is V_(dq), and has acontrollable magnitude (0≦V_(dq)≦V_(dqmax)) and angle (0≦ρ≦360°). Theinserted voltage V_(dq) is added to the fixed sending-end voltage,V_(s), to produce the effective sending-end voltage, V_(o)=V_(s)+V_(dq).The difference, V_(o)−V_(r), provides the compensated voltage, V_(x),across X_(L). As angle ρ is varied over its full 360° range, the end ofphasor V_(dq) moves along a circle with its center located at the end ofphasor V_(s). The rotation of phasor V_(dq) with angle ρ modulates boththe magnitude and the angle of phasor V_(x) and, therefore, both thetransmitted real power, P, and the reactive power, Q, vary with ρ in asinusoidal manner.

This process, of course, requires the compensating voltage, V_(dq), tosupply and absorb both real and reactive power, P_(exch) and Q_(exch),which are also sinusoidal functions of angle ρ, as shown in FIG. 16.Since the compensating voltage is derived from the line voltage througha transformer action with the primary winding, the exchanged real andreactive power with the line must flow through the primary winding tothe line. Since the series injected voltage is, typically, only a fewpercent of the line voltage, the shunt current would be the same fewpercent of the line current. The current through the exciter unit hasboth real and reactive components. The loading effect of these twocurrents on the power system network is independent of each other asshown. Therefore, if it is desirable to compensate the combined loadingeffects of the real and the reactive current through exciter unit intothe AC system, a separate shunt connected reactance compensator may beconsidered.

Note that with the VPFT of the present invention, impedance compensationmay be performed by appropriately setting the compensating resistancedemand, R*, and the compensating reactance demand, X*, at the controllerto minimize system fault current. In particular, the VPFT and thecontroller in such a situation measure the magnitude of the line currentto determine if it exceeds a predetermined level, and upon suchdetermination, the VPFT controllably injects the maximum amount ofinductive reactance in series with the transmission line until the faultclears and then reestablishes the controlled compensation. Note alsothat with the VPFT of the present invention, the transformer leakagereactance can be kept to a minimum possible value.

The main differences between a UPFC as shown in FIG. 12 and a VPFT asshown in FIG. 14 are as follows:

a. In a UPFC, only the real component of the power exchanged by theseries injected compensating voltage with the transmission line flowsback to the line through the DC link capacitor and the shunt connectedconverter, STATCOM. The real current of such real component alters thevoltage at the point of connection of STATCOM with the transmissionline. The voltage of the transmission line may be controlledindependently by regulating the reactive current flow through theSTATCOM. In a VPFT, both the real and the reactive power exchanged bythe series injected compensating voltage with the transmission line flowback to the line through the exciter unit. The real and reactivecomponents of the current of such power flow transformer alter thevoltage at the point of connection of the exciter unit with thetransmission line. The loading effect of such currents on the powersystem network is independent of each other. Therefore, if it isdesirable to compensate the combined loading effects of the real and thereactive current through the exciter unit into the power system network,a separate shunt connected reactance compensator may be considered.

b. The UPFC has the capability of fast response in sub-cycle time.However, such capability is not used in a power system applicationbecause step-injection of voltage in a transmission line may causeunwanted disturbances in the power system including instability. TheVPFT has a response that is limited by the speed of the mechanical orsolid state tap changer, which is quite adequate for most utilityapplications. Of course, dynamic performance can be improved, whenneeded, by replacing a mechanical tap changer with a solid state tapchanger such as the thyristor-controlled switches of FIG. 3.

c. In a UPFC, only 10-15% of the cost is estimated to be intransformers. The remainder is in delicate power electronics andaccessories. The cost of the same rated VPFT is estimated to be about20% that of a UPFC.

The main differences between a PAR as discussed in connection with FIGS.10A-10E and a VPFT as shown in FIG. 14 are as follows:

a. In a PAR, the effective phase angle of the line voltage is varied byinjecting a series voltage in quadrature with the phase-to-neutralvoltage of the transmission line. The effect is such that both the realand the reactive power flow in the line are changed simultaneously. In aVPFT, the injected voltage is at any angle with respect to theprevailing line current and, therefore, emulates in series with the saidtransmission line, a capacitor, an inductor, a positive resistor thatabsorbs real power from the line and a negative resistor that deliversreal power to the line. The effect is such that both the real and thereactive power flow in the line are changed selectively just like aUPFC. In addition, a VPFT can regulate the line voltage by utilizing theunused portions of the transformer windings, thereby not requiring anyextra hardware.

b. In order to realize the functions of regulating the real and thereactive power flow in the line selectively and regulating the linevoltage, a VPFT employs only one single-core three-phase transformer. Ina PAR, the same functions are realized by using two transformers, onefor direct voltage injection and the other for quadrature voltageinjection.

c. In a PAR configuration, it is not possible to place taps on theprimary side of the regulating transformer because of the shorting thatoccurs when zero insertion voltage is needed. In an improved version ofa VPFT, discussed below, the taps are indeed placed on the primary sideof the transformer. The magnitude of the composite voltage can bechanged between zero and the maximum voltage that any of the windingscan offer. Note that If the maximum voltages induced in all threewindings (a1, a2 and a3) are combined, the composite voltage is zero.This property makes it possible to move all the taps to the exciter unitand to keep the series compensating unit relatively simple. The taps canbe operated during a normal flow of line current and a high faultcurrent.

It is to be appreciated that the VPFT of the present invention may bemodified to be employed in other multi-phase transmission line schemes,including four-phase, five-phase, six-phase, etc. For example, for asix-phase scheme, the VPFT would have six primary windings and eachprimary winding would have six secondary windings for a total ofthirty-six secondary windings. Further details of such a multi-phaseVPFT should be apparent to the relevant public and therefore need not bedescribed herein in any detail.

Following are variations of the VPFT as disclosed above and inconnection with FIGS. 14-16.

Shunt Compensating Transformer

In one variation of the present invention, the VPFT is operated as ashunt-compensating transformer such as the shunt-compensatingtransformer discussed above in connection with FIG. 2. In particular,and as seen in FIG. 17, the VPFT of FIG. 14 is operated to inject acompensating in-phase (0 degrees) or out-of-phase (180 degrees) voltageof line frequency in series with the line through an auto-transformeraction so as to regulate the magnitude of the line voltage at a point ina transmission line, but not alter the phase of such line voltage.

As with the VPFT of FIG. 14, the line voltage is applied to ashunt-connected single-core three-phase transformer's primary windings.Also as with the VPFT of FIG. 14, the compensating voltage in any phaseis derived from the induced voltages on three windings, each of which isplaced on the transformer core of a different phase. Here, the positive(in-phase) compensating voltage for any phase is derived solely from thewinding placed on the corresponding phase of the transformer core, andthe negative (out-of-phase) compensating voltage for such phase isderived from the vectorial sum of an equal number of turns of the othertwo windings.

In particular, and as seen in FIG. 17, in the shunt compensatingtransformer, the line voltage is applied across the primary windings 1A,IB, 1C in the exciter unit (only winding 1A being shown). Each primarywinding has three secondary windings in series, for a total of ninesecondary windings—a1, c2 and b3 on the core of A-phase; b1, a2 and c3on the core of B-phase; and c1, b2 and a3 on the core of C-phase. Asseen, a compensating voltage for any phase is derived from the vectorialsum of the voltages induced in a three-phase winding set—a1, a2 and a3for injection in A-phase; b1, b2 and b3 for injection in B-phase; andc1, c2 and c3 for injection in C-phase. A tap is employed on each of thenine secondary windings so that each entity in each vectorial sum can beindividually magnitudally varied, although it is to be appreciated thatto regulate the magnitude of the line voltage at a point in atransmission line while at the same time not altering the phase of suchline voltage, the mutual settings of the taps are necessarilyrestricted.

As with the VPFT of FIG. 14, in the shunt compensating transformer ofFIG. 17, the voltage V_(21A) (shown) is:

V _(21A)=%x a 1+%y a 2+%z a 3;

and voltage V_(21A) is injected as a compensating voltage in line withv_(1A) to produce compensated voltage V_(2A):

V _(2A) =V _(21A) +V _(1A).

Compensating voltages V_(21B) for the B-phase and V_(21C) for theC-phase are similarly produced:

V _(21B)%x b 1+%y b 2+%z b 3;

V _(2B) =V _(21B+V) _(1B).

V _(21C)%x c 1+%y c 2+%z c 3;

V _(2C) =V _(21C) +V _(1C).

Importantly, to produce an in-phase or out-of-phase compensating voltagein the shunt compensating transformer, %y and %z are set to besubstantially equal such that the vector(al sum of each of %y a2+%z a3,%y b2+%z b3, and %y c2+%z c3 is out-of-phase with %x a1, %x b1, and %xc1, respectively. As should be appreciated, then, the resulting voltagesV_(21A), V_(21B), V_(21C), are either in-phase or out-of-phase withrespect to V_(1A), V_(1B), V_(1C), respectively.

Preferably, to produce an in-phase compensating voltage in the shuntcompensating transformer, %y and %z are set to be substantially zero.Also preferably, to produce an out-of-phase compensating voltage in theshunt compensating transformer, %x is set to be substantially zero and%y and %z are set to be substantially equal.

The controller of the control block diagram of FIG. 15 may also beemployed in connection with the shunt compensating transformer of FIG.17, although such controller is not strictly necessary since only themagnitude of V₁ is being altered.

Once the compensating voltage demand V_(dq)* and whether thecompensating voltage is to be in- or out-of-phase have been defined, andwith knowledge of the limitation that %y and %z are to be substantiallyequal, the Tap Control Unit in FIG. 15 determines the contribution fromeach winding of a 3-phase set (a1, a2, and a3 for injection in A-phase;b1, b2, and b3 for injection in B-phase; and c1, c2, and c3 forinjection in C-phase) to constitute V_(dq)* . In particular, fromknowledge of the magnitude of the exciter voltage, V₁, the Tap ControlUnit determines the number of turns necessary on each winding of theseries-compensating unit. The actual method of such determination isknown or should be apparent to the relevant public and therefore neednot be discussed herein in any detail. Based on this calculation, theappropriate taps are switched on via an appropriate mechanical or solidstate tap changer (see FIG. 3, e.g.), which accordingly put the requirednumber of turns in series with the line. Of course, other methods ofcontrolling the shunt compensating transformer of FIG. 17 may beemployed without departing from the spirit and scope of the presentinvention.

As with the VPFT of FIG. 14, it is to be appreciated that the shuntcompensating transformer of FIG. 17 may be modified to be employed inother multi-phase transmission line schemes, including four-phase,five-phase, six-phase, etc. Details of such a multi-phaseshunt-compensating transformer should be apparent to the relevant publicand therefore need not be described herein in any detail.

The shunt compensating transformer of FIG. 17 injects a compensatingvoltage in series with the line either in- or out-of-phase with the linevoltage. As may be appreciated, the compensating voltage is at any anglewith the prevailing line current. Accordingly, and as with the VPFT ofFIG. 14, the compensating voltage of the shunt compensating transformerof FIG. 17 exchanges real and reactive power with the line. Since thecompensating voltage is derived from the line voltage through atransformer action with the primary winding, the exchanged real andreactive power with the line must flow through the primary winding tothe line. Since the series injected voltage is, typically, only a fewpercent of the line voltage, the shunt current would be the same fewpercent of the line current.

Series Compensating Transformer

In another variation of the present invention, the VPFT of FIG. 14 isoperated as a series compensating transformer. In particular, and asseen in FIG. 18, the VPFT of FIG. 14 is operated to inject acompensating voltage of line frequency in series with the line throughan auto-transformer action so as to regulate both the magnitude andphase of the line voltage at a point in a transmission line.

As with the VPFT of FIG. 14, the line voltage is applied to ashunt-connected single-core three-phase transformer's primary windings.Also as with the VPFT of FIG. 14, the compensating voltage in any phaseis derived from the induced voltages on three windings, each of which isplaced on the transformer core of a different phase. Here, by choosingthe number of turns of each of the three windings, and therefore themagnitudes of the components of the three induced voltages, thecomposite series injected voltage magnitude and angle with respect tothe transmission line voltage is selected. The compensating voltage canbe at any angle with the prevailing line current, which emulates, inseries with the line, a capacitor that increases the power flow of theline or an inductor that decreases the power flow of the line and apositive resistor that absorbs real power from the line or a negativeresistor that delivers real power to the line. The effect is such thatthe real and the reactive power flow in a transmission line can beregulated selectively. As a special case, the compensating voltage canbe in quadrature with the phase-to-neutral voltage of the transmissionline, thereby regulating the effective phase angle of the line voltage.

In particular, and as seen in FIG. 18, in the series compensatingtransformer, the line voltage is applied across the primary windings 1A,1 B, 1 C in the exciter unit (only winding 1A being shown). Each primarywinding has three secondary windings in series, for a total of ninesecondary windings—a1, c2 and b3 on the core of A-phase; b1, a2 and c3on the core of B-phase; and c1, b2 and a3 on the core of C-phase. Asseen, a compensating voltage for any phase is derived from the vectorialsum of the voltages induced in a three-phase winding set—a1, a2 and a3for injection in A-phase; b1, b2 and b3 for injection in B-phase; andc1, c2 and c3 for injection in C-phase. A tap is employed on each of thenine secondary windings so that each entity in each vectorial sum can beindividually magnitudally varied. It is to be appreciated that in theseries compensating transformer of FIG. 18, and in contrast with theshunt compensating transformer of FIG. 17, mutual settings of the tapsare different in the series compensating transformer of FIG. 18 so thatit regulates both the magnitude and phase of the line voltage at a pointin a transmission line.

As with the VPFT of FIG. 14, in the series compensating transformer ofFIG. 18, the voltage V_(21A) (shown) is:

V _(21A)=%x a 1+%y a 2+%z a 3;

and voltage V_(21A) is injected as a compensating voltage in line withv_(1A) to produce compensated voltage V_(2A):

V _(2A) =V _(21A) +V _(1A).

Compensating voltages V_(21B) for the B-phase and V_(21C) for theC-phase are similarly produced:

V _(21B)=%x b 1+%y b 2+%z b 3;

V _(2B) =V _(21B) +V _(1B).

V _(21C)=%x c 1+%y c 2+%z c 3;

V _(2C) =V _(21C) +V _(1C).

The controller of the control block diagram of FIG. 15 may also beemployed in connection with the series compensating transformer of FIG.18. Such controller or a variation thereof is necessary inasmuch as boththe magnitude and phase of V₁ is being altered. Accordingly, thecontroller controlling the series compensating transformer is concernedwith the required magnitude alteration (i.e., the desired seriesinjection voltage, V_(dq)*), and with the angle β of FIG. 15.

Once the desired series injection voltage V_(dq)* and angle β aredefined, the Tap Control Unit in FIG. 15 determines the contributionfrom each winding of a 3-phase set (a1, a2, and a3 for injection inA-phase; b1, b2, and b3 for injection in B-phase; and c1, c2, and c3 forinjection in C-phase) to constitute the defined V_(dq)* and β. Inparticular, from knowledge of the magnitude of the exciter voltage, V₁,the Tap Control Unit determines the number of turns necessary on eachwinding of the series-compensating unit. The actual method of suchdetermination is known or should be apparent to the relevant public andtherefore need not be discussed herein in any detail. Based on thiscalculation, the appropriate taps are switched on via an appropriatemechanical or solid state tap changer (see FIG. 3, e.g.), whichaccordingly put the required number of turns in series with the line. Ofcourse, other methods of controlling the series compensating transformerof FIG. 18 may be employed without departing from the spirit and scopeof the present invention.

The series compensating transformer of FIG. 18 injects a compensatingvoltage in series with the line at any angle with respect to the linevoltage. The compensating voltage is at any angle with respect to theline voltage and line current. This requires the compensating voltage toexchange real and reactive power with the line. Since the compensatingvoltage is derived from the line voltage through a transformer actionwith the primary winding, the exchanged real and reactive power with theline must flow through the primary winding to the line. Since the seriesinjected voltage is, typically, only a few percent of the line voltage,the shunt current would be the same few percent of the line current.Thus, the real and the reactive power flow in a transmission line can beregulated selectively. A special case of an injection angle of 90° isachieved by using a Phase Angle Regulator (PAR) that injects a voltagein quadrature with the phase-to-neutral voltage of the transmissionline.

As with the VPFT of FIG. 14, it is to be appreciated that the seriescompensating transformer of FIG. 18 may be modified to be employed inother multi-phase transmission line schemes, including four-phase,five-phase, six-phase, etc. Details of such a multi-phaseseries-compensating transformer should be apparent to the relevantpublic and therefore need not be described herein in any detail.

Limited Injection Angle Series Compensating Transformers

In another variation of the present invention, the VPFT of FIG. 14 isoperated as a series compensating transformer with limited injectionangle regulation. In particular, and as seen in FIGS. 19-21, the VPFT ofFIG. 14 is operated as a series compensating transformer such as that inFIG. 18, except that each primary winding has less than three secondarywindings.

In some applications, it may not be necessary to be able to inject aseries voltage at any angle between 0 to 360°. In an application wherethere is a need for injecting a voltage between 0 and −120°, aseries-compensating transformer with only 6 windings as shown in FIG. 19may be employed. As seen, the 0 to −120° angle is achieved byconstructing the series injection voltage from a combination of twoseries voltages, each of which is induced in a separate winding of a2-phase set.

Here, the line voltage is applied across the primary windings 1A, 1B, 1Cin the exciter unit (only winding 1A being shown). Each primary windinghas two secondary windings in series, for a total of six secondarywindings—a1 and c2 on the core of A-phase; b1 and a2 on the core ofB-phase; and c1 and b2 on the core of C-phase. A compensating voltagefor any phase is derived from the vectorial sum of the voltagesinduced—a1 and a2 for injection in A-phase; b1 and b2 for injection inB-phase; and c1 and c2 for injection in C-phase. Once again, a tap isemployed on each secondary winding so that each entity in each vectorialsum can be individually magnitudally varied. Thus, the voltage V_(21A)(shown) is:

V _(21A)=%x a 1+%y a 2.

V_(21B) and V_(21C) are similarly produced:

V _(21B)=%x b 1+%y b 2; and

V _(21C)=%x c 1+%y c 2.

Similarly, in an application where there is a need for injecting avoltage between 0 and 120°, a series-compensating transformer with only6 windings as shown in FIG. 20 may be employed. As seen, the 0 to 120°angle is also achieved by constructing the series injection voltage froma combination of two series voltages, each of which is induced in aseparate winding of a 2-phase set.

Here, the six secondary windings are—a1 and b3 on the core of A-phase;b1 and c3 on the core of B-phase; and c1 and a3 on the core of C-phase.A compensating voltage for any phase is derived from the vectorial sumof the voltages induced—a1 and a3 for injection in A-phase; b1 and b3for injection in B-phase; and c1 and c3 for injection in C-phase. Thus,the voltages are:

V _(21A)=%x a 1+%z a 3.

V _(21B)=%x b 1+%z b 3; and

V _(21C)=%x c 1+%z c 3.

In an application where there is a need for injecting a voltage between120° and 240° a series-compensating transformer with only 6 windings asshown in FIG. 21 may be employed. Here, the six secondary windingsare—c2 and b3 on the core of A-phase; a2 and c3 on the core of B-phase;and b2 and a3 on the core of C-phase. A compensating voltage for anyphase is derived from the vectorial sum of the voltages induced—a2 anda3 for injection in A-phase; b2 and b3 for injection in B-phase; and c2and c3 for injection in C-phase. Thus, the voltages are:

V _(21A)=%y a 2+%z a 3.

V _(21B)=%y b 2+%z b 3; and

V _(21C)=%y c 2+%z c 3.

Extending the concept just presented, the polarities of the windings inthe series-compensating transformer of FIG. 21 can be reversed toprovide a phase angle regulation between −60° and 60°, as is shown inFIG. 22. In the same way, if the polarities of the windings in theseries compensating transformers of FIGS. 19 and 20 are reversed (notshown), then phase angle regulation between 60° and 180° and between180° and 300°, respectively, is achieved.

The controller of the control block diagram of FIG. 15 may also beemployed in connection with the transformers of FIGS. 19-22 in a mannerthat should now be apparent to the relevant public.

Reverse VPFT Transformer

In another variation of the present invention, the VPFT of FIG. 14 isoperated such that the primaries and secondaries thereof are reversed.In particular, and as seen in FIG. 23, in such a reverse VPFTtransformer, the VPFT of FIG. 14 is operated as a series compensatingtransformer there are three secondary windings, one for each phase, andthree primary windings for each secondary winding for a total of nineprimary windings.

Each phase of the primary voltage is applied across any or all of threewindings, each of which is placed on the transformer core of a differentphase. The compensating voltage for series injection in any phase isinduced in a single secondary winding. This secondary winding and threecorresponding primary windings excited from three different phasevoltages are placed on the respective phase of the exciter core. Bychoosing the number of turns in each of the three primary windings, andtherefore the magnitudes of the components of the three primary windingvoltages, the composite series injected voltage's magnitude and anglewith respect to the transmission line voltage can be of selected.

As with the series compensating transformer of FIG. 18, for example, thecompensating voltage can be at any angle with the prevailing linecurrent and therefore emulates, in series with the line, a capacitorthat increases the power flow of the line or an inductor that decreasesthe power flow of the line and a positive resistor that absorbs realpower from the line or a negative resistor that delivers real power lothe line. The effect is such that the real and the reactive power flowin a transmission line can be regulated selectively. In addition, and aswith the shunt compensating transformer of FIG. 17, for example, thereverse transformer can regulate the line voltage by utilizing theunused portions of the transformer windings as a shunt compensatingunit.

As seen at section (a) of FIG. 23, a phasor diagram for the reversetransformer shows a three-phase line voltage V_(A,B,C). The voltage,v_(1A), is applied across three windings a1, a2 and a3. The voltage,v_(1B), is applied across three windings b1, b2 and b3. The voltage,V_(1c), is applied across three windings c1, c2 and c3. The number ofturns of each of a1, a2, a3, b1, b2, b3, c1, c2, and c3 is individuallycontrolled by a mechanical or solid state tap changer such as the tapchanger shown in FIG. 3. The composite voltage from the three windings(al, c2 and b3) on the primary side (exciter unit) is reflected on thesecondary side (series unit) in A-phase. Likewise, the composite voltagefrom the three windings (b1, a2 and c3) is reflected on the secondaryside in B-phase, and the composite voltage from the three windings (c1,b2 and a3) is reflected on the secondary side in C-phase. Depending onthe number of turns chosen on the three windings (a1, c2 and b3), (b1,a2 and c3), (c1, b2 and a3),the series injection voltage's magnitude andangle are determined.

Put mathematically,

V _(21A) =N(%x a 1+%y c 2+%z b 3);

V _(21B) =N(%x b 1+%y a 2+%z c 3); and

V _(21C) =N(%x c 1+%y b 2+%z a 3).

where N is a constant based on the turns ratios between the primarywindings and the secondary winding.

For example, in section (b) of FIG. 23, a phasor diagram shows theexciter voltage is applied across one winding in each phase only. Theseries injection voltage is in phase with the line voltage and itsmagnitude is dependent on the number of turns in the series winding andthe winding a1. Thus, the reverse transformer is acting as a shuntcompensating transformer such as that shown in FIG. 17.

Correspondingly, in section (c) of FIG. 24, a phasor diagram shows theexciter voltage is applied across three windings a1, a2 and a3 withpre-determined numbers of turns. The series injection voltage V₂₁ isthus the vectorial sum of the voltages across the three windingsmultiplied by the turns ration N. Thus, the reverse transformer isacting as a series compensating transformer such as that shown in FIG.18. If, as shown the numbers of turns are equal, the sum is zero withsame number of turns, the series injection voltage is the vectorial sumof three equal voltages with 120° phase difference from one another.That is, the sum is zero. The same principle applies to the other twophases of series injection voltage as well.

The controller of the control block diagram of FIG. 15 may also beemployed in connection with the reverse transformer in a manner thatshould now be apparent to the relevant public. Of course, othercontrollers may be employed without departing from the spirit and scopeof the present invention.

Notably, just as the series compensating transformer of FIG. 18 may belimited in operation to certain phase angles, as was discussed inconnection with FIGS. 19-22, so too may the reverse VPFT transformer belimited in operation to certain phase angles by similar machinations.Such machinations should now be apparent to the relevant public,especially in view of the discussed in connection with FIGS. 19-22, andtherefore need not be described herein in any further detail.

In the reverse transformer of FIG. 23, the compensating voltage V₂₁ isof variable magnitude and at any angle with respect to the line voltage.The real or direct component of the compensating voltage provides thevoltage regulation; whereas the reactive or quadrature componentprovides the phase angle regulation. The compensating voltage can alsobe at any angle with respect to the prevailing line current. The real ordirect component of the compensating voltage provides the seriesresistance emulation; whereas the reactive or quadrature componentprovides the series reactance emulation. The resistance emulator can beused to dampen oscillations, which may be created by an existingcapacitor in the transmission system. The reactance emulator can be usedto provide the reactance compensation of the transmission line. All ofthe transmission parameters can be regulated simultaneously by injectinga resultant series voltage, which can be derived from the line voltageand, in turn, the real and the reactive power flow in the line can beregulated selectively. The compensating voltage V₂₁ is always of linefrequency and does not induce sub-synchronous resonance.

The tap-changer technology-based reverse transformer injects a seriesvoltage of variable magnitude at any angle with respect to theprevailing line current as well as line voltage. The compensatingvoltage exchanges both real and reactive power with the line. Since thecompensating voltage is derived from the line voltage through atransformer action with the primary winding, the exchanged real andreactive power with the line must flow through the primary winding tothe line. Since the series injected voltage is, typically, only a fewpercent of the line voltage, the shunt current would be the same fewpercent of the line current. The current through the exciter unit hasboth real and reactive components. The loading effect of these twocurrents on the power system network is independent of each other.Therefore, if it is desirable to compensate the combined loading effectof the real and the reactive current through exciter unit into the powersystem network, a separate shunt connected reactance compensator may beconsidered.

Conclusion

The hardware necessary to effectuate the present invention, such as thetransformers and tap changers, is known or should be readily apparent tothe relevant public. Accordingly, further details as to the specifics ofsuch hardware are not believed to be necessary herein. The programmingnecessary to effectuate the present invention, such as the programmingrun by the controller of FIG. 15, is likewise known or should be readilyapparent to the relevant public. Accordingly, further details as to thespecifics of such programming are also not believed to be necessaryherein.

As should now be understood, in the present invention, a versatile powerflow transformer (VPFT) and variations thereof are based on thetraditional technologies of transformers and tap changers, and areemployed to selectively control the real and the reactive power flow ina line and regulate the voltage of the transmission line. Such VPFTgenerates a compensating voltage of line frequency for series injectionwith a transmission line. Such compensating voltage is extracted fromthe line voltage and is of variable magnitude and at any angle withrespect to the line voltage. The compensating voltage is also at anyangle with respect to the prevailing line current, which emulates, inseries with the line, a capacitor that increases the power flow of theline or an inductor that decreases the power flow of the line and apositive resistor that absorbs real power from the line or a negativeresistor that delivers real power to the line. Accordingly, the real andthe reactive power flow in a transmission line can be regulatedselectively. Changes could be made to the embodiments described abovewithout departing from the broad inventive concepts thereof. It isunderstood, therefore, that this invention is not limited to theparticular embodiments disclosed, but it is intended to covermodifications within the spirit and scope of the present invention asdefined by the appended claims.

What is claimed is:
 1. A limited-angle power flow transformer forimplementing power flow control in a transmission line of an n-phasepower transmission system, each phase of the power transmission systemhaving a transmission voltage, the transformer comprising: n primarywindings, each primary winding on a core, each primary winding forreceiving the transmission voltage of a respective one of the phases ofthe power transmission system; m secondary windings on the core of eachprimary winding for a total of m*n secondary windings, m being less thann, each secondary winding for having a voltage induced thereon by thecorresponding primary winding, for each phase, m secondary windingsbeing assigned to the phase, each assigned secondary winding for thephase being from a different core, for all phases, the secondarywindings being assigned from the cores in a balanced manner, for eachphase, the secondary windings assigned to the phase being coupled inseries for summing the induced voltages formed thereon, wherein thesummed voltage is a compensating voltage for the phase, and wherein thecompensating voltage is angularly limited with respect to the phase, foreach phase, the in-series secondary windings being further coupled inseries with the primary winding corresponding to the phase, wherein thecompensating voltage is added to the transmission voltage of the phaseto result in a compensated voltage for the phase.
 2. The transformer ofclaim 1 wherein the compensating voltage supplies and absorbs both realand reactive power.
 3. The transformer of claim 1 for implementing powerflow control in a transmission line of a 3-phase (A, B, C) powertransmission system, the transformer comprising: 3 primary windings; 2secondary windings on the core of each primary winding for a total of 6secondary windings: secondary windings a1 and c2 on the core of theprimary winding associated with A-phase; secondary windings b1 and a2 onthe core of the primary winding associated with B-phase; and secondarywindings c1 and b2 on the core of the primary winding associated withC-phase; a1 and a2 being coupled in series for summing the inducedvoltages formed thereon, such summed voltage for compensating thevoltage on A-phase; b1 and b2 being coupled in series for summing theinduced voltages formed thereon, such summed voltage for compensatingthe voltage on B-phase; and c1 and c2 being coupled in series forsumming the induced voltages formed thereon, such summed voltage forcompensating the voltage on C-phase.
 4. The transformer of claim 3further comprising an adjustable tap changer coupled to each secondarywinding, each tap changer for individually magnitudally varying theinduced voltage formed on the corresponding secondary winding, whereinthe compensating voltage V_(21A) for A-phase, the compensating voltageV_(21B) for B-phase, and the compensating voltage V_(21C) for C-phaseare: V _(21A)=%x a 1+%y a 2; V _(21B)=%x b 1+%y b 2; and V _(21C)=%x c1+%y c 2, %x and %y each being set according to the tap changerswinding, and wherein, for each phase, the summed voltage is angularlyadjustable in a limited manner by adjusting the tap changers of thephase.
 5. The transformer of claim 4 wherein %x and %y are each setbetween 0 and 1 according to the tap changers.
 6. The transformer ofclaim 4 wherein %x and %y are each set between −0.5 and 0.5 according tothe tap changers.
 7. The transformer of claim 3 wherein a1, b1, and c1are substantially identical; and a2, b2, and c2 are substantiallyidentical.
 8. The transformer of claim 1 for implementing power flowcontrol in a transmission line of a 3-phase (A, B, C) power transmissionsystem, the transformer comprising: 3 primary windings; 2 secondarywindings on the core of each primary winding for a total of 6 secondarywindings: secondary windings a1 and b3 on the core of the primarywinding associated with A-phase; secondary windings b1 and c3 on thecore of the primary winding associated with B-phase; and secondarywindings c1 and a3 on the core of the primary winding associated withC-phase; a1 and a3 being coupled in series for summing the inducedvoltages formed thereon, such summed voltage for compensating thevoltage on A-phase; b1 and b3 being coupled in series for summing theinduced voltages formed thereon, such summed voltage for compensatingthe voltage on B-phase; and c1 and c3 being coupled in series forsumming the induced voltages formed thereon, such summed voltage forcompensating the voltage on C-phase.
 9. The transformer of claim 8further comprising an adjustable tap changer coupled to each secondarywinding, each tap changer for individually magnitudally varying theinduced voltage formed on the corresponding secondary winding, whereinthe compensating voltage V_(21A) for A-phase, the compensating voltageV_(21B) for B-phase, and the compensating voltage V_(21C) for C-phaseare: V _(21A)=%x a 1+%z a 3; V _(21B)=%x b 1+%z b 3; and V _(21C)=%x c1+%z c 3, %x and %z each being set according to the tap changerswinding, and wherein, for each phase, the summed voltage is angularlyadjustable in a limited manner by adjusting the tap changers of thephase.
 10. The transformer of claim 9 wherein %x and %z are each setbetween 0 and 1 according to the tap changers.
 11. The transformer ofclaim 9 wherein %x and %z are each set between −0.5 and 0.5 according tothe tap changers.
 12. The transformer of claim 8 wherein a1, b1, and c1are substantially identical; and a3, b3, and c3 are substantiallyidentical.
 13. The transformer of claim 1 for implementing power flowcontrol in a transmission line of a 3-phase (A, B, C) power transmissionsystem, the transformer comprising: 3 primary windings; 2 secondarywindings on the core of each primary winding for a total of 6 secondarywindings: secondary windings c2 and b3 on the core of the primarywinding associated with A-phase; secondary windings a2 and c3 on thecore of the primary winding associated with B-phase; and secondarywindings b2 and a3 on the core of the primary winding associated withC-phase; a2 and a3 being coupled in series for summing the inducedvoltages formed thereon, such summed voltage for compensating thevoltage on A-phase; b2 and b3 being coupled in series for summing theinduced voltages formed thereon, such summed voltage for compensatingthe voltage on B-phase; and c2 and c3 being coupled in series forsumming the induced voltages formed thereon, such summed voltage forcompensating the voltage on C-phase.
 14. The transformer of claim 13further comprising an adjustable tap changer coupled to each secondarywinding, each tap changer for individually magnitudally varying theinduced voltage formed on the corresponding secondary winding, whereinthe compensating voltage V_(21A) for A-phase, the compensating voltageV_(21B) for B-phase, and the compensating voltage V_(21C) for C-phaseare: V _(21A)=%y a 2+%z a 3; V _(21B)=%y b 2+%z b 3; and V _(21C)=%y c2+%z c 3, %y and %z each being set according to the tap changerswinding, and wherein, for each phase, the summed voltage is angularlyadjustable in a limited manner by adjusting the tap changers of thephase.
 15. The transformer of claim 14 wherein %y and %z are each setbetween 0 and 1 according to the tap changers.
 16. The transformer ofclaim 14 wherein %y and %z are each set between −0.5 and 0.5 accordingto the tap changers.
 17. The transformer of claim 13 wherein a2, b2, andc2 are substantially identical; and a3, b3, and c3 are substantiallyidentical.
 18. A limited-angle power flow transformer for implementingpower flow control in a transmission line of an n-phase powertransmission system, each phase of the power transmission system havinga transmission voltage, the transformer comprising: n primary windings,each primary winding on a core, each primary winding for receiving thetransmission voltage of a respective one of the phases of the powertransmission system; m secondary windings on the core of each primarywinding for a total of m * n secondary windings, m being less than n,each secondary winding for having a voltage induced thereon by thecorresponding primary winding, for each phase, m secondary windingsbeing assigned to the phase, each assigned secondary winding for thephase being from a different core, for all phases, the secondarywindings being assigned from the cores in a balanced manner, for eachphase, the secondary windings assigned to the phase being coupled inseries for summing the induced voltages formed thereon, wherein thesummed voltage is a compensating voltage for the phase, and wherein thecompensating voltage is angularly limited with respect to the phase, thetransformer further comprising an adjustable tap changer coupled to eachsecondary winding, each tap changer for individually magnitudallyvarying the induced voltage formed on the corresponding secondarywinding, wherein, for each phase, the secondary windings assigned to thephase as magnitudally varied by the respective tap changers are coupledin series for summing the magnitudally varied induced voltages formedthereon, and wherein, for each phase, the summed voltage is angularlyadjustable in a limited manner by adjusting the tap changers of thephase, the transformer still further comprising a controller forcontrolling the tap changers, the controller receiving as inputs thetransmission voltage of each phase of the power transmission system, aset of measured line currents, a compensating resistance demand, R*, anda compensating reactance demand, X*.
 19. The transformer of claim 18wherein the compensating voltage is adjustable to any angle within arange of r with respect to line voltage, r=(m−1)*360/n, the transformerthereby being capable of emulating in series with the transmission lineat least one of an inductor, a capacitor, a positive resistor thatabsorbs real power from the line and/or a negative resistor thatdelivers real power to the line.
 20. The transformer of claim 18 whereineach tap changer is selected from a group consisting of a mechanical tapchanger or a solid-state tap changer.
 21. The transformer of claim 18wherein the controller has: a first magnitude/angle calculator forcalculating a magnitude, v1, and a reference angle, Q, of thetransmission line from the transmission voltage of each phase of thepower transmission system; a second magnitude/angle calculator forcalculating a magnitude, I, and a relative angle, Qir, with respect to Qof the line current based on the set of measured line currents; ademanded impedance calculator for calculating a magnitude, Z*, andangle, Qz, of a demanded impedance based on the compensating resistancedemand, R*, and the compensating reactance demand, X*; an insertionvoltage magnitude demand calculator for calculating an insertion voltagemagnitude demand, V_(dq)*, based on the magnitude, I, of the linecurrent as multiplied by the demanded impedance magnitude, Z*; arelative phase angle demand calculator for calculating a relative phaseangle demand, b, based on the sum of Qir and Qz; and a tap control unitfor adjusting the tap changers based on Vdq*, b, and V1.